Exam 11: Functions

Solve the problem. -The number of mosquitoes $\mathrm { M } ( \mathrm { x } )$ , in millions, in a certain area depends on the June rainfall $\mathrm { x }$ , in inches, according to the function $\mathrm { M } ( \mathrm { x } ) = 20 \mathrm { x } - \mathrm { x } ^ { 2 }$ . What rainfall produces the maximum number of mosquitoes?

Find the x- and y-intercepts. If no x-intercepts exist, state so. - $f ( x ) = x ^ { 2 } + 16 x$

For the functions f(x) and g(x), evaluate the indicated function. -Find $( f + g ) ( - 4 )$ when $f ( x ) = x - 7$ and $g ( x ) = x - 1$ .

For the given functions f(x) and g(x), find (f ∙ g)(x) or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f ( x ) = x ^ { 2 } + 4$

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value - $f ( x ) = - ( x + 5 ) ^ { 2 } - 1$

Solve the problem. - $f ( x ) = \sqrt { x + 5 }$

Solve the problem. -A cable TV company charges $28 for the basic service plus $5 for each movie channel. Find a linear function f(x) = mx + b whose input is the number of movie channels selected and whose output is The total cost. Find the slope-intercept form of the equation.

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2. -Shift 10 units to the right and 14 units down.

For the functions f(x) and g(x), evaluate the indicated function. -The number of male lawyers, in thousands, in a certain country in a particular year can be approximated by the function f(x) = 11.4x + 214, where x represents the number of years after 1985. The number of female lawyers , in thousands, in a certain country in a particular year can be Approximated by the function g(x) = 10.3x + 162, where again x represents the number of years After 1985. (i) Find (f + g)(x). Explain, in your own words, what this function represents. (ii) Find (f + g)(40). Explain, in your own words, what this number represents.

Find the vertex. - $f ( x ) = - ( x + 1 ) ^ { 2 } - 3$

For the functions f(x) and g(x), evaluate the indicated function. -Find $( f - g ) ( 5 )$ when $f ( x ) = - 5 x ^ { 2 } + 6$ and $g ( x ) = x - 3$ .

Given f(x) and g(x), find the indicated composition and evaluate. - $f ( x ) = - 5 x + 6 ; g ( x ) = 4 x ^ { 2 } - 8 x + 7$ Find $( \mathrm { f } \cdot \mathrm { g } ) ( 7 )$ .

Without graphing the function, state the shift(s) that are applied to the graph of f(x) = x2 to graph the given function. If the graph of f(x) = x2 must be rotated about the x-axis, state this. - $f ( x ) = ( x + 8 ) ^ { 2 }$

Solve the problem. - $f ( x ) = ( x - 10 ) ^ { 2 } + 2 ( x \geq 10 )$

Given f(x) and g(x), find the indicated composition and evaluate. - $f ( x ) = 7 x + 3 ; g ( x ) = x + 6$ Find $( f \circ g ) ( 2 )$ .

Given f(x) and g(x), find the indicated composition and state its domain. - $f ( x ) = 4 x ^ { 2 } + 2 x + 4 , g ( x ) = 2 x - 7$ Find $( g \circ f ) ( x )$ .

Given f(x) and g(x), find the indicated composition and state its domain. -For $\mathrm { f } ( \mathrm { x } ) = 8 \sqrt { \mathrm { x } + 2 }$ and $\mathrm { g } ( \mathrm { x } ) = 4 \mathrm { x } + 10$ , what is the domain of $\mathrm { f } \cdot \mathrm { g }$ ?

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2. -Shift 13 units down.

Solve the problem. -Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c ( x ) = 2 x ^ { 2 } - 200 x + 87$ , where $x$ is the number of watches repaired. How many watches must he repair to have the lowest cost?

Find the x- and y-intercepts. If no x-intercepts exist, state so. - $f ( x ) = x ^ { 2 } + 6 x + 9$